Low Noise Ultrathin Freestanding Membranes Composed of Atomically-Thin 2D Materials

ABSTRACT

The invention provides methods for direct growth of low noise, atomically thin freestanding membranes of two-dimensional monocrystalline or polycrystalline materials, such as transition metal chalcogenides including molybdenum disulfide. The freestanding membranes are directly grown over an aperture by reacting two precursors in a chemical vapor deposition process carried out at atmospheric pressure. Membrane growth is preferentially over apertures in a thin sheet of solid state material. The resulting membranes are one or a few atomic layers thick and essentially free of defects. The membranes are useful for sequencing of biopolymers through nanopores.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a divisional application of U.S. application Ser. No. 15/552,373filed 21 Aug. 2017 as the national phase of PCT/US2015/062686 filed 25Nov. 2015, which claims the priority of U.S. Provisional Application No.62/118,795 filed 20 Feb. 2015 and of U.S. Provisional Application No.62/119,675 filed 23 Feb. 2015. Each of the aforementioned applicationsis hereby incorporated by reference in its entirety.

BACKGROUND

The ability to exfoliate single- and few-layer graphene flakes from bulkgraphite opened up new avenues into the physics of two-dimensionalmaterials. [1,2] Even though graphene is a good electrical and thermalconductor, its zero band gap property hinders the possibilities in awide range of potential applications in next generation nanoelectronicsand optoelectronics. [3] Moreover, engineering a band gap of graphenemakes the fabrication more complicated and reduces the electronicmobility. [4,5] In this regard, molybdenum disulfide (MoS₂), a layeredtransition metal dichalcogenide (TMDC), in which unsaturated d-electroninteractions can give rise to new interesting material properties, hasgarnered a great interest in many next generation nanotechnologyapplications due to its fascinating electrical, optical and mechanicalproperties. [6] MoS₂, a semiconductor with a finite band gap, iscomposed of covalently bonded S—Mo—S sheets that are bound by weak vander Waals forces. The band gap of MoS₂ can be tuned from direct (˜1.8eV) [7] to indirect (˜1.0 eV) [8] in its bulk and monolayer forms,respectively. It has been investigated that the band structure and bandgap of MoS₂ are strongly affected by quantum confinement due to itsatomically thin two-dimensional crystal structure. [9-11] The band gapof MoS₂ can be modified either by reducing the number of layers[9,11-14] or by applying a large local uniaxial strain to thefilm/membrane [15]. The tunable band gap of the MoS₂ makes it promisingfor applications in optoelectronic devices, such as photodetectots,[16,17] photovoltaics, [18], photocatalysts and light emitters [19].

An indirect to direct band gap transition from multilayer to monolayerresults in pronounced enhancement in photoluminescence (PL) [9,12] dueto a very high quantum yield for monolayer MoS₂, which affirms theoptical band gap at around 1.9 eV [9,10,12]. While bulk MoS₂ has aprominent direct band gap, PL in the bulk is nonexistent owing toexcitonic absorption, yet when the direct band gap is dominant, forinstance in monolayer regime, direct band radiative recombinationbecomes the principle method for exciton recombination. [12] It has beenfound that PL quantum yields for monolayer MoS₂ is about 3 ordersgreater than that of multilayer structure due to radiative recombinationacross the direct band gap. The PL quantum yield is greatly enhancedwhen the monolayer MoS₂ is suspended. [9] PL of MoS₂ is substantiallyaffected by the nature of the substrate/interface, which may haveeffects on material performance. [20]

The atomically thin two-dimensional structure of MoS₂ films/membranesnot only opens up new avenues in nanoelectronic and optoelectronicapplications but also high surface-to-area ratios. These uniquecharacters make few-layer MoS₂ flakes promising sensing devices to manyadsorbates. In contrast to brittle bulk phase, mono- and few-layer MoS₂flakes have superior elasticity and flexibility and hence are promisingfunctional membranes. [21] For instance, a laminar separation membraneassembled from atomically thin MoS₂ sheets exhibits a water permeancewhich is 3-5 orders higher than that of graphene oxide membranes. [22]

Bertolazzi et. al recently measured elastic modulus and breakingstrength of mono and bilayer MoS₂ membranes exfoliated from bulk andtransferred onto an array of micro fabricated circular holes in asubstrate. [23] According to their measurements, in-plane stiffness ofmonolayer MoS₂ is 180±60 Nm⁻¹ and an effective Young's modulus of270±100 GPa, which is comparable to that of steel. These unique materialproperties of mono and multilayer MoS₂ sheets might make them suitablefor a variety of applications such as reinforcing elements in compositesand for fabrication of flexible electronic devices. For example, severalgroups recently developed flexible field-effect transistors (FETs) basedon the large in-plane carrier mobility, robust mechanical properties,flexible and transparent nature, and low power dissipation ofmono/few-layer MoS₂. [11,24,25] Further, monolayer MoS₂ has recentlybeen utilized as a material for microelectromechanical systems (MEMS)and nanoelectromechanical systems (NEMS) devices. [1,9,11,26] Recently,a few research groups demonstrated the use of monolayer and multilayerMoS₂ in integrated circuits, although they were only in proof-of-conceptstage. [27,28] MoS₂ has recently garnered a lot of interest inbiosensing applications due to its two-dimensional crystal structure,electronic properties, tunable band gap, high thermal and chemicalstability. [29] Especially, MoS₂ has been utilized in electrochemicaldevices [30-32] and also in field-effect-transistor (FET) devices[33,34] to use as a biosensor for rapid and high-resolution biosensingapplications. Ultrathin membranes are ideal candidates forbase-resolution nanopore based DNA sequencing applications, becauseatomically thin membrane can amplify the baseline current and also theamplitude of the transient current drop without increasing the noiselevel, which results in a great enhancement in signal-to-noise SNR)ratio. In addition to the great enhancement in ionic current amplitude,transverse tunneling current can also be used for high-resolutionelectronic base detection. [35-37] This goal could be achieved using 2Dmaterials like graphene [38-41] and transition metal dichalcogenides,for example MoS₂ [42,43] and boron nitride [44]. Several groups haverecently shown high-resolution DNA detection using mono- and few-layergraphene nanopores [38-41], yet the large noise compared to traditionaldielectric material based nanopores and the zero band gap property ofgraphene hinder the development of graphene-based nanopore sensors toachieve base-resolution detection. Even though a finite band gap can beengineered in pristine graphene, this increases the fabricationcomplexity and reduces the electronic mobility. The greater noiseinherent with atomically thick single layer graphene can be reduced byusing three-layer thick graphene (about 1 nm), which consequentlyincreases the signal-to-noise ratio. In this perspective, atomicallythin (about 0.8 nm) MoS₂ is a better alternative for graphene providinga better signal-to-noise ratio while maintaining its atomically thickproperty for base-resolution DNA detection. Another issue with graphenenanopores is that DNA sticks a lot to the pore wall as well as thesurface during the translocation process due the strong r-r interactionbetween graphene and DNA, which could prove very challenging fornucleobase detection experiments via transverse tunneling current. Incontrast, atomically thick MoS₂ can be engineered to have either Mo(molybdenum) or S (sulfur) or both Mo and S terminated sheets, whichopens up a new avenue for base-resolution detection experiments.

Few-layer or even mono-layer MoS₂ flakes can be exfoliated from bulkcrystalline material. Such flakes are widely used in research as theypossess perfect crystalline structure as well as pristine quality.However, mechanical exfoliation is an extremely low yield process, whichin general results in flakes a few micrometers to a few tens ofmicrometers in size. Therefore, the mechanical exfoliation approach ishandicapped with respect to large-scale, high-quality flake fabrication.Chemical exfoliation is also another well-recognized exfoliationapproach, which was known well before mechanical exfoliation. [45,46]There are two types of chemical exfoliation approaches, ionintercalation (the Morrison method) [45] and solvent-based exfoliation(the Coleman method) [47]. The Morrison method is handicapped by somemajor difficulties, such as relatively high temperature requirement(100° C.) and lengthy reaction time (three days), while the Colemanmethod suffers from low-yield of single-layer sheets and low MoS₂ flakeconcentration in solution. The chemical vapor deposition (CVD) methodhas gained great interest for fabricating mono- and few-layer MoS₂sheets due to its ease of synthesis and high efficiency, together withits wide tolerance for growth parameters and substrates. [48-54]

In order to investigate the pristine material characterization of MoS₂sheets, it is essential to have less-contaminated freestanding MoS₂sheets over a freestanding window. Further, it is vital to synthesizehigh quality freestanding MoS₂ membranes for use in membrane-basedapplications such as nanopore devices, selective molecular sievingdevices, gas sensors and other semiconductor devices. To date,production of freestanding MoS₂ requires transfer of MoS₂ sheets to anappropriately perforated substrate, which often introduces contaminantsas well as unintentional wrinkles, cracks and tears into the sheets. Inaddition to the degradation of the quality of the MoS₂ sheets, thetransfer process is extremely low-yield and is not scalable to a wholewafer such that there is sufficient amount of membrane surface area foruse in membrane related experiments.

SUMMARY OF THE INVENTION

The invention provides novel methods for direct growth of freestandingmembranes formed from two-dimensional (2D) materials, such as transitionmetal chalcogenides including molybdenum disulfide (MoS₂), acrosssolid-state apertures; the materials formed using these methods havenovel properties. The freestanding membranes are directly grown over anaperture by reacting two reactants, such as molybdenum trioxide (MoO₃)or molybdenum dioxide (MoO₂) and sulfur (S), in a chemical vapordeposition (CVD) process carried out at atmospheric pressure.Surprisingly, low-noise ultrathin membranes of the 2D material growpreferentially over apertures, resulting in intact pristine membranesthat are one or a few layers thick. The mechanism by which this occursis believed to be related to a thermal gradient that develops around theaperture, which favors aperture-limited growth.

According to the present invention, in situ fabrication of freestandingmembranes onto a perforated substrate does not require transferringsheets of 2D material after its synthesis. As a consequence, the formedmembrane retains its pristine quality with no contamination, resultingin ideal substrates for material characterization and membrane-basedapplications. Compared to prior methods of producing flakes of suchmaterials and then transferring them to a suitable structure for devicefabrication, the approach of the invention is more practical forobtaining large amounts of membrane with high yield.

One aspect of the invention is an ultrathin membrane containing atwo-dimensional material. The membrane spans an aperture in a sheet ofsolid state material and is attached to a surface of the sheet in anarea surrounding the aperture.

Another aspect of the invention is a method of fabricating an ultrathinmembrane containing a two-dimensional material. The method includes thestep of performing chemical vapor deposition of a first membraneprecursor disposed on a first side of a sheet of solid state materialincluding an aperture and a second membrane precursor disposed on asecond side of the sheet, whereby the ultrathin membrane is formed fromthe first and second precursors across the aperture and contacts asurface of the sheet of solid state material in an area surrounding theaperture.

Still another aspect of the invention is a method of detecting amolecule. The method includes the steps of: (a) providing an ultrathinmembrane as described above containing a nanopore, the membrane mountedin a device having electrolyte solution on both sides of the ultrathinmembrane, an electrode in each electrolyte solution, and a device formeasuring ionic currents through the nanopore; (b) measuring a baselineionic current through the nanopore; and (c) observing blockage of thebaseline ionic current by the molecule to detect the molecule, which ispresent in one of the electrolyte solutions.

The invention can be further summarized by the following list of items.

1. An ultrathin membrane comprising a two-dimensional material, themembrane spanning an aperture in a sheet of solid state material andattached to a surface of the sheet in an area surrounding the aperture.2. The ultrathin membrane of item 1, wherein the two-dimensionalmaterial is selected from the group consisting of GaS, GaSe, InS, InSe,HfS₂, HfSe₂, HfTe₂, MoS₂, MoSe₂, MoTe₂, NbS₂, NbSe₂, NbTe₂, NiS₂, NiSe₂,NiTe₂, PdS₂, PdSe₂, PdTe₂, PtS₂, PtSe₂, PtTe₂, ReS₂, ReSe₂, ReTe₂, TaS₂,TaSe₂, TaTe₂, TiS₂, TiSe₂, TiTe₂, WS₂, WSe₂, WTe₂, ZrS₂, ZrSe₂, andZrTe₂.3. The ultrathin membrane of item 2, consisting essentially of MoS₂ orMoSe₂.4. The ultrathin membrane of any of the preceding items, wherein thetwo-dimensional material is essentially monocrystalline.5. The ultrathin membrane of any of the preceding items, wherein themembrane consists essentially of from one to several atomically thinsheets of the two-dimensional material.6. The ultrathin membrane of any of the preceding items, wherein thethickness of the membrane is 1-2 atomic layers.7. The ultrathin membrane of any of the preceding items, wherein thethickness of the membrane is from about 0.7 nm to about 10 nm.8. The ultrathin membrane of any of the preceding items having a densityof holes and atomic vacancies in the range from 0 to about 10 per nm².9. The ultrathin membrane of any of the preceding items, which isessentially free of holes and atomic vacancies.10. The ultrathin membrane of any of the preceding items having aspecific conductance in the range from about 0.2 to about 1000 nS/μm².11. The ultrathin membrane of any of the preceding items having aspecific conductance of less than about 0.2 nS/μm².12. The ultrathin membrane of any of the preceding items, wherein theaperture has a diameter from about 0.02 μm to about 2 μm.13. The ultrathin membrane of any of the preceding items, wherein themembrane spans a plurality of apertures.14. The ultrathin membrane of item 13, wherein the plurality ofapertures is arranged in a two-dimensional array.15. The ultrathin membrane of any of the preceding items, wherein thesheet of solid state material has a thickness in the range from about 5nm to about 10 μm.16. The ultrathin membrane of any of the preceding items, wherein thesolid state material comprises a material selected from the groupconsisting of silicon nitride, silicon dioxide, hafnium oxide, titaniumoxide, and aluminum oxide.17. The ultrathin membrane of any of the preceding items, wherein thesheet of solid state material is mounted on a support structure.18. The ultrathin membrane of item 17, wherein the support structurecomprises silicon.19. The ultrathin membrane of any of the preceding items, furthercomprising one or more nanopores, each nanopore having a diameter in therange from about 0.3 nm to about 50 nm.20. The ultrathin membrane of item 19 having an ion current noise levelof less than 400 pA at 200 kHz bandwidth.21. The ultrathin membrane of any of the preceding items, wherein themembrane spans a plurality of apertures, and wherein the membranecomprises one or more nanopores within each aperture.22. The ultrathin membrane of item 21, wherein the diameters of thenanopores are in the range from about 0.3 nm to about 50 nm.23. The ultrathin membrane of item 21 configured for use as a waterfilter.24. The ultrathin membrane of item 21 configured for use in biomoleculesequencing.25. A method of fabricating the ultrathin membrane of any of thepreceding items, the membrane comprising a two-dimensional material, themethod comprising the step of performing chemical vapor deposition of afirst membrane precursor disposed on a first side of a sheet of solidstate material comprising an aperture and a second membrane precursordisposed on a second side of the sheet, whereby said ultrathin membraneis formed from the first and second precursors across the aperture andcontacting a surface of the sheet of solid state material in an areasurrounding the aperture.26. The method of item 25, wherein the first membrane precursorcomprises a metal selected from the group consisting of Ga, In, Hf, Mo,Nb, Ni, Pd, Pt, Re, Ta, Ti, W, and Zr.27. The method of item 26, wherein the first membrane precursor is anoxide of said metal.28. The method of any of items 25-27, wherein the second membraneprecursor comprises S, Se, or Te.29. The method of any of items 25-28, wherein the two-dimensionalmaterial formed is selected from the group consisting of GaS, GaSe, InS,InSe, HfS₂, HfSe₂, HfTe₂, MoS₂, MoSe₂, MoTe₂, NbS₂, NbSe₂, NbTe₂, NiS₂,NiSe₂, NiTe₂, PdS₂, PdSe₂, PdTe₂, PtS₂, PtSe₂, PtTe₂, ReS₂, ReSe₂,ReTe₂, TaS₂, TaSe₂, TaTe₂, TiS₂, TiSe₂, TiTe₂, WS₂, WSe₂, WTe₂, ZrS₂,ZrSe₂, and ZrTe₂.30. The method of item 29, wherein the two-dimensional material consistsessentially of MoS₂ or MoSe₂.31. The method of any of items 25-30, wherein said chemical vapordeposition comprises heating the first membrane precursor and secondmembrane precursor in separate containers and in the presence of aninert carrier gas.32. The method of item 31, wherein the container comprising the firstmembrane precursor is disposed near the first side of said sheet ofsolid state material, the container comprising the second membraneprecursor is disposed remotely from said sheet of solid state material,and the heated second membrane precursor is carried towards the apertureby the carrier gas at the second side of said sheet of solid statematerial; and wherein the ultrathin membrane is fabricated on a surfaceof the sheet on the second side.33. The method of item 27, wherein atoms of the second membraneprecursor displace oxygen atoms of the oxide and form a two-dimensionalmaterial at the aperture.34. The method of any of items 25-33, wherein the first and secondmembrane precursors are heated to about 650 to 800° C. at about 3 to 10°C./min under carrier gas flow, and held at about 650 to 800° C. forabout 15 to 60 minutes.35. The method of item 34 wherein, prior to said heating step, the firstand second membrane precursors are heated to about 300 to 400° C. at arate of about 20 to 30° C./min under carrier gas flow and held at about300 to 400° C. for about 15 to 30 minutes.36. The method of any of items 25-35, wherein said carrier gas flow ismaintained at a rate of about 180 to 200 sccm.37. The method of any of items 25-36, wherein said inert carrier gas isAr or N₂.38. The method of any of items 25-37, wherein the ultrathin membrane isfabricated across an aperture having a diameter of from about 0.02 μm toabout 2.0 μm.39. The method of any of items 25-38, wherein the solid state materialis a material selected from the group consisting of silicon nitride,silicon dioxide, hafnium dioxide, titanium dioxide, and aluminum oxide.40. The method of any of items 25-39, wherein the thickness of theultrathin membrane is 1-2 atomic layers.41. The method of any of items 25-40, wherein the ultrathin membrane isessentially free of holes and atomic vacancies.42. The method of any of items 25-41, wherein the ultrathin membraneconsists essentially of monocrystalline MoS₂ or MoSe₂.43. The method of any of items 25-42, further comprising the step offorming one or more nanopores in the ultrathin membrane.44. The method of item 43, wherein the one or more nanopores are formedusing an electron beam, an ion beam, a laser, or application of voltageacross the membrane.45. The method of any of items 43-44, wherein the one or more nanoporeseach have a diameter in the range from about 0.3 nm to about 50 nm.46. A method of detecting a molecule, the method comprising the stepsof:

(a) providing the ultrathin membrane of item 19 mounted in a devicehaving electrolyte solution on both sides of the ultrathin membrane, anelectrode in each electrolyte solution, and a device for measuring ioniccurrents through a nanopore of the ultrathin membrane, wherein theelectrolyte solution on one side of the ultrathin membrane comprisessaid molecule for detection;

(b) measuring a baseline ionic current through said nanopore; and

(c) observing blockage of the baseline ionic current by said molecule.

47. The method of item 46, wherein the molecule is a nucleic acid or aprotein.48. The method of any of items 46-47, wherein the molecule is detectedas it moves through the nanopore of said ultrathin membrane.49. The method of any of items 46-48, wherein a nucleotide sequence oran amino acid sequence of the molecule is determined.50. The method of item 48, wherein a protein is detected, and theprotein reduces the ionic current through the nanopore for about 2 msecto about 5 msec.51. The method of any of items 46-50, wherein the ultrathin membrane isfunctionalized in a region surrounding the nanopore with afunctionalization moiety having a binding affinity for said molecule.52. The method of item 51, wherein the functionalization moiety is anenzyme or an antibody.53. The method of any of items 46-52, wherein at least one of saidelectrolyte solutions comprises an ionic species, the other of saidelectrolyte solutions comprises a fluorescent indicator that binds saidionic species and changes its fluorescence in response thereto, and acurrent through the nanopore carried by said ion is detected via thefluorescence of the indicator.54. The method of item 53, wherein the ion is Ca²⁺.55. A device comprising at least one ultrathin membrane of any of items1-24.56. The device of item 55, wherein the ultrathin membrane comprises oneor more nanopores.57. The device of any of items 55-56 comprising at least 100 of saidultrathin membranes, each comprising one or more nanopores.58. The device of any of items 55-57 configured to measure ionicconductance across the one or more nanopores individually.59. The device of any of items 55-58 configured to optically measure ionfluxes through the one or more nanopores using a fluorescent indicator.60. The device of any of items 55-59 configured to measure a vibrationof the ultrathin membrane.61. The device of any of items 55-60 configured as a sensor.62. The device of item 56 configured as a filter.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a schematic illustration of an aperture-limitedfreestanding ultrathin membrane fabrication process. A sheet of solidstate material that contains a micron-scale hole (or array of holes) isplaced over a boat containing a first membrane precursor in a quartzfurnace. After an initial sublimation of the first membrane precursormaterial, temperature and carrier gas flow are adjusted such that asublimated second membrane precursor material flows over the aperture.FIG. 1B shows a schematic illustration of a proposed mechanism by whichaperture-limited growth of membrane occurs. Elements in the figure arenot to scale. FIG. 1C shows further detail of the proposed mechanism.FIG. 1D shows a schematic illustration of a portion of a filter deviceof the invention.

FIGS. 2A-2C show characterization by electron microscopy of MoS₂membranes. FIG. 2A shows bright-field (BF) transmission electronmicroscopy (TEM) images of the CVD-assisted fabricated freestanding MoS₂membranes over micron-scale holes fabricated in silicon nitride (SiN)sheets. Panels (i)-(iv) show BF-TEM images of four different MoS₂membranes grown across micron-scale holes. The inset of a (i) shows thelithography assisted pattern written in the SiN sheet before MoS₂ growthby CVD. FIG. 2B shows high-resolution TEM (HRTEM) images of thefreestanding MoS₂ membrane collected from the highlighted region inpanel (i) shown with a dashed box. Panel (ii) shows single-layer andbilayer domains of MoS₂ in the SiN sheet across an approximately 6×6 nm²area. Panel (iii) shows an HRTEM image of a single-layer MoS₂ membranecorresponding to the domain highlighted in the dashed box in panel (ii).The upper inset shows the corresponding diffractogram of the monolayer.The bottom portion shows a line-profile scanned across 10 latticepoints. The lattice constant of the (100) plane was 0.27 nm. Panel (iv)shows an HRTEM image of a bilayer MoS₂ domain from the area highlightedin the dashed box in panel (ii). The inset shows the correspondingdiffractogram of bilayer MoS₂. FIG. 2C shows BF-TEM images of adifferent device with a five submicron hole pattern after MoS₂ growth,where four holes are completely covered with MoS₂ sheets. Panels(ii)-(iv) show BF-TEM images at different magnifications of one of thethree holes as highlighted in the dashed box, which is completelycovered with freestanding MoS₂ membrane. The different contrasts are dueto the thickness variation of the MoS₂ membrane. The ripples in the MoS₂membranes, which are due to strain applied on the SiN sheets, canclearly be seen in FIG. 2C (iii).

FIGS. 3A-3C show scanning transmission electron microscopy (STEM) imagesand secondary electron (SE) images of the device shown in FIG. 2A. FIG.3A shows a STEM image of the same device shown in FIG. 2a , whichconfirms that MoS₂ grows on the trans side of the membrane (i.e., sidethat faces away from the MoO₃ boat). FIG. 3B shows a backscattering modeimage of the same device, which further verifies that MoS₂ grows on thetrans side of the membrane. FIG. 3C shows a high-resolution STEM imageof a MoS₂ membrane collected in the highlighted region (dashed box) inFIG. 3A. The inset shows a diffraction pattern computed from the rightside of the membrane, which corresponds to MoS₂ bilayer structure.

FIG. 4A shows Raman characterization of MoS₂ membranes. The Ramanspectra were collected in the vicinity of the center hole in the deviceshown in FIG. 2A, which corresponds to MoS₂ sheets that are 2-3 layersthick. FIG. 4B shows a Raman spectrum of a molybdenum diselenide (MoSe₂)membrane grown on the aperture shown inside the dashed line box of theinset. The Raman spectrum was collected in from the area inside the box.The inset shows an optical image of the MoSe₂ membrane deposited on anaperture-containing freestanding SiN sheet.

FIG. 5 shows an atomic resolution image of a freestanding 10 nm×20 nmregion of a MoS₂ membrane. The inset shows the FFT spectrum of theimage.

FIGS. 6A-6C show ion transport measurements through nanopores in MoS₂membrane devices. FIG. 6A shows a schematic representation of the deviceused for ion current measurements. FIG. 6B shows current-voltage curvesof several nanopores (0.40 M KCl, pH 8, T=21° C., pore diameter d andconductance G indicated in legend). The current-voltage curve for d=0 isthe horizontal line, and for d=16.3 nm is the line with greatest slope;the other lines have intermediate slopes proportional to the area of thenanopore. The inset shows a TEM image of several pores drilled adjacentto each other (scale bar=5 nm). FIG. 6C shows a comparison ofexperimental G and d values with theoretical curves computed for 1 to 4MoS₂ layers.

FIG. 7A shows ion current noise power spectral densities (PSD) for aMoS₂ membrane containing a 2.8 nm diameter pore at different appliedvoltages (the applied voltages range from 0 (bottom) to 200 mV (top) atthe left side of the figure). The solution was 0.40M KCl, pH 8, T=21° C.FIG. 7B shows PSD plots for an ultrathin graphene membrane containing a7.5 nm diameter pore at 0 mV (bottom curve at left side) and 200 mV (topcurve at left side) applied voltages. The graphene 1/f noise at 200 mVexceeded the MoS₂ noise by an order of magnitude (compare noise valuesat 100 Hz in FIGS. 6A and 6B).

FIGS. 8A and 8B show detection of the transport of single-stranded DNAmolecules through a 2.3 nm diameter MoS₂ nanopore. FIG. 8A shows athree-second continuous current trace for a 2.3 nm diameter pore afterthe addition of 20 nM of 153-mer ssDNA to the cis chamber ([KCl]=0.40 M,V_(trans)=200 mV, sampling rate=4.17 MHz, data low-pass filtered to 200kHz). Concatenated sets of events at different magnifications are shownbelow the trace. FIG. 8B shows a scatter plot of fractional currentblockade vs. dwell time td, as well as histograms of each parametershown on each corresponding axis (n=number of molecules detected).

FIG. 9A shows calmodulin transport through a nanopore (22 nm diameter)in an ultra-thin MoS₂ membrane. A continuous 1.5 s long current trace isshown. Calmodulin was present at 100 nM in the solution, and transportof calmodulin through the nanopore can be seen as downward spikes. Biasvoltage was 100 mV. Inset shows an expanded view of representativecalmodulin translocation events. FIG. 9B shows a histogram of timeintervals between events. The capture rate (Rc) of calmodulintranslocations is shown in the legend, which is the inverse of the timeconstant of the time interval distribution (solid diagonal line). FIG.9C shows a scatter plot of the magnitude of current blockades vs. dwelltime for 165 calmodulin translocation events (sampling rate=4.2 MHz,low-pass filtered at 50 kHz, T=25° C., 0.4 M KCl, pH 7.8).

DETAILED DESCRIPTION OF THE INVENTION

The invention provides freestanding ultrathin membranes oftwo-dimensional (2D) materials having unique properties including apristine, monocrystalline or polycrystalline morphology that is robustand essentially free of defects, and provides exceptionally lowelectrical noise when measuring ionic currents through nanopores forbiomolecule sequencing applications. The membranes are fabricated by anovel chemical vapor deposition process that produces aperture-dependentgrowth of a variety of 2D materials and avoids the need to transferflakes of such materials to an aperture for various applications, withconsequent introduction of structural defects and contamination. Thefabrication process can provide membranes of large surface area,rendering them useful for water filtration applications. The membranesof the present invention also can be used as components of electronicdevices, such as FETs or components of MEMS or NEMS devices.

An exemplary fabrication method is summarized by the fabrication schemeshown in FIGS. 1A and 1B. First, substrate or support structure 10(e.g., silicon chips, optionally coated with a layer of silicon oxide20) having window 33, over which is deposited a thin freestanding sheet30 of a solid state material (e.g., 30-50 μm² of SiN of 100 nmthickness), is hot piranha cleaned and dried with a gentle flow ofnitrogen (N₂) gas, followed by warm deionized (DI) water rinsing. Next,positive electron beam resist is spun onto the cleaned and dried chip,and then one or more micron-scale apertures (optionally an array of suchapertures) are written on the freestanding SiN membrane using e-beamlithography and subsequently developed.

Then, SiN is controllably etched through the apertures in SiN membraneusing an SF₆ reactive ion etch (RIE) plasma to produce one or morecorresponding apertures 32 in the SiN sheet. Subsequently, the resist isstripped off using an acetone bath and hot piranha treatment. Afreestanding membrane of 2D material, such as MoS₂, then can be growndirectly onto the aperture or pre-patterned array of apertures in theSiN sheet to form membrane device 100. For example, the membrane can begrown using molybdenum trioxide (MoO₃) and sulfur (S) as precursors in achemical vapor deposition (CVD) process carried out at 750-800° C. andatmospheric pressure. In such a CVD process, first membrane precursor 4(e.g., MoO₃ powder) is placed into boat 4-1 or other container in theCVD furnace, and second membrane precursor 2 (e.g., sulfur powder) isplaced into boat 2-1 or other container in the CVD furnace.

The placement of the membrane precursor materials in the furnace isimportant. The prepared freestanding solid state sheet with itssupporting substrate is placed above the first membrane precursorcontainer such that sublimating first membrane precursor can rise up andcontact the aperture in the solid state sheet where membrane fabricationis desired. The second membrane precursor container is placed upstreamof the first membrane precursor container with respect to the flow ofinert carrier gas 5, such that sublimating second membrane precursorrises up and is carried toward the aperture for membrane formation bythe carrier gas. The flow of carrier gas is arranged so that the secondmembrane precursor is delivered by the carrier gas to the opposite sideof the aperture from the side contacted by sublimating first membraneprecursor. The membrane is formed on the side of the aperture to whichthe second membrane precursor is delivered; that side is referred to asthe “trans” side of the device, the other side being the “cis” side.

FIG. 1C presents a model of the mechanism of membrane formation.Transition metal atoms 1 from the first membrane precursor accumulate onthe underside (i.e., the cis side) of the sheet of solid state material30 and inside of aperture 32. Atoms 3 of second membrane precursoraccumulate on the upper side (i.e., the trans side) of the sheet. Bothsets of atoms react and build membrane 40 at the trans side. Themembrane structures depicted in FIG. 1C are nucleation structures whichgrow from the perimeter inwards toward the center to complete themembrane. While membrane formation is aperture limited, i.e., it occurspreferentially at apertures in the solid state sheet material, thefinished membrane not only covers the aperture completely but alsocovers the trans side solid state sheet in a region surrounding theaperture, forming a leak-proof seal. If membrane growth is allowed tocontinue, membrane formation can continue at the trans side of the sheetand fuse to form a continuous sheet of membrane covering the sheet.

When the membrane fabrication process is allowed to form a continuoussheet of membrane, e.g., covering a plurality of apertures or an arrayof apertures, the resulting structure can form a filter device, aportion of which is depicted in FIG. 1D. In such a device, solid statesheet 30 containing apertures 32 is covered by a continuous sheet of 2Dmembrane 40, which provides a sieving effect, for example, allowingwater molecules to penetrate but holding back dissolved solutes.Optionally, one or more nanopores can be introduced into the membrane ateach aperture to provide pathways for desired solutes to pass throughthe filter, depending on their size or other molecular properties. Inaddition, the membrane and/or nanopores can be functionalized orchemically modified in order to confer selectivity to the molecularsieving effect of the filter.

The membrane can have a polycrystalline or monocrystalline structure andis preferably atomically thin, i.e., containing 1, 2, 3, 4, 5, 6, 7, 8,9, or 10 layers of 2D material. Preferably, the membrane has a thicknessin the range from about 0.7 nm to about 10 nm. For example, the membranethickness can be less than 10, 9, 8, 7, 6, 5, 4, 3, 2, or 1 nm. Inpreferred embodiments, the membrane has 1 or 2 layers (i.e., 1-2 atomiclayers) of 2D material, or a mixture of regions having 1 and regionshaving 2 layers. For example, a MoS₂ membrane having 1 atomic layerrefers to a 2D monocrystalline or polycrystalline arrangement having asingle layer of MoS₂ molecules, and it is understood that such a singlelayer may have sublayers of Mo and S atoms as dictated by the crystalstructure. In certain preferred embodiments, the membrane is free ofholes, atomic vacancies, or other structural defects over the entirearea of membrane covering the aperture. In other preferred embodiments,the membrane contains 10 or fewer, 9 or fewer, 8 or fewer, 7 or fewer, 6or fewer, 5 or fewer, 4 or fewer, 3 or fewer, 2 or fewer, or 1 or fewerholes or atomic vacancies per nm² of membrane area covering theaperture. The density of holes or atomic vacancies can be controlledduring fabrication in order to produce desired properties, such asdesired molecular size cutoff in filtration.

A variety of 2D materials, i.e., materials that form atomically thinmonocrystalline or polycrystalline two dimensional sheets, can be usedto form the membrane. Such materials include GaS, GaSe, InS, InSe, HfS₂,HfSe₂, HfTe₂, MoS₂, MoSe₂, MoTe₂, NbS₂, NbSe₂, NbTe₂, NiS₂, NiSe₂,NiTe₂, PdS₂, PdSe₂, PdTe₂, PtS₂, PtSe₂, PtTe₂, ReS₂, ReSe₂, ReTe₂, TaS₂,TaSe₂, TaTe₂, TiS₂, TiSe₂, TiTe₂, WS₂, WSe₂, WTe₂, ZrS₂, ZrSe₂, andZrTe₂. The 2D materials can be, for example, transition metalchalcogenides or semimetal chalcogenides. Preferred 2D materials for themembrane are MoS₂ and MoSe₂. Suitable membrane materials can befabricated in an aperture-limited fashion by CVD from two or moremembrane precursor materials. The membrane precursor materials can beany chemical precursor of the membrane material compatible with theconditions required for CVD, and which react under the conditions of CVDto produce the membrane material in an aperture-limited fashion.Required properties of the precursor materials include thermal stabilityto several hundred degrees C. and ability to sublimate at suchtemperatures and bind the solid state sheet at the aperture.

In some embodiments, the device contains a substrate or supportstructure attached to the sheet of solid state material that carries themembrane. The support structure contains a window that provides accessof fluid to the membrane. In some embodiments, the device contains aninsulating layer disposed between the support structure and the sheet ofsolid state material. The supporting structure can comprise or consistof silicon, silicon dioxide, glass, quartz, or mica. In preferredembodiments, the support structure is silicon. The insulating layer cancomprise or consist of silicon dioxide, glass, quartz, or mica. Inpreferred embodiments, the support structure is silicon, coated in wholeor in part by an insulating layer of silicon dioxide. In someembodiments, the support structure and the insulating layer, if present,contain a plurality of windows, each window providing access to at leastone well. In some embodiments the support structures contain one or morescored lines between two or more windows, the scored lines enabling thedivision of the device into two or more pieces, each piece containingone or more windows. In some embodiments, the device has at least 5, atleast 10, at least 20, at least 50, at least 100, at least 150, or atleast 200 windows.

The sheet of solid state material comprises or consists of siliconnitride, silicon dioxide, aluminum oxide, titanium oxide, or hafniumoxide. The sheet has a thickness in the range from about 5 nm to about10 μm. In preferred embodiments, the substrate is about 100 nm thick.The sheet of solid state material contains one or more apertures coveredby membrane of 2D material. The apertures are generally circular, butcould have another shape. The apertures have a diameter, or largestdimension across, in the range from about 0.02 μm to about 2 μm. In someembodiments, each aperture has a diameter of less than 2 μm, less than1.5 μm, less than 1.2 μm, less than 1 μm, less than 750 nm, less than500 nm, less than 400 nm, less than 300 nm, less than 200 nm, or lessthan 100 nm.

The invention includes an apparatus for the study of polymers, such asbiopolymers, including polynucleotides, polypeptides, peptides,proteins, oligosaccharides, and polysaccharides, as they are transportedthrough nanopores in a 2D material membrane. An embodiment of such anapparatus is depicted in FIG. 6A. Apparatus 110 includes nanoporemembrane device 100, wherein membrane 40, containing nanopore 50, ispositioned between first fluid reservoir 301 and second fluid reservoir302; an electrode pair having first electrode 401 disposed in the firstfluid reservoir and second electrode 402 disposed in the second fluidreservoir; voltage source 403 for establishing a voltage between theelectrodes; and circuit 404 capable of detecting an electrical signal(e.g., ionic current through the nanopore) that correlates with thesequence of the polymer, or another aspect of the polymer molecule. Themembrane device can be attached via adhesive layers 300 and 310 to firstand second chambers (200 and 210 respectively), which can beconstructed, for example, of a chemically inert polymer material such asPTFE, or of silicon, silicon dioxide, or quartz.

The membranes of the present invention are essentially free ofstructural defects. Defects such as cracks, holes, and atomic vacanciesmay allow ions or other solutes to pass through the membrane, therebyinterfering with uses of the membrane including measuring ionic currentto characterize polymers, and filtration. The presence of an intactmembrane can be inferred from low specific conductance of the membrane.For example, while testing using a 1M or 0.4M solution of KCl at roomtemperature, the specific conductance may be less than 0.1 nS/μm², lessthan 0.2 nS/μm², less than 0.3 nS/μm², less than 0.5 nS/μm², less than0.7 nS/μm², less than 1 nS/μm², less than 1.5 nS/μm², less than 2nS/μm², less than 5 nS/μm², less than 10 nS/μm², or less than 20 nS/μm².Higher values of conductance can be useful in certain applications, suchas selective filtration designed to trap only specific solutes orclasses of solutes. Generally, the specific conductance is in the rangefrom about 0.2 nS/μm² to about 1000 nS/μm². In a preferred embodiment,the specific conductance is less than 0.2 nS/μm² when measured using0.4M KCl. With membranes of the present invention, the backgroundelectrical noise from the membrane itself, e.g., when measuring ioniccurrents through a nanopore in the membrane, is preferably less than 400pA at 200 kHz bandwidth (i.e., low-pass filtered at 200 kHz).

Because the fabrication method of the present invention avoids transferof the membrane after fabrication, the method reliably produces intactmembranes that are free of cracks. For example, the percentage of intactmembranes produced by the method may be greater than 60%, greater than70%, greater than 80%, greater than 85%, greater than 90%, greater than95%, greater than 98%, or greater than 99%. Whether a membrane is intactmay be determined, for example, from its ionic conductance. Thus, amembrane may considered intact if the ionic conductance across themembrane is less than 0.1 nS/μm², less than 0.3 nS/μm², less than 0.5nS/μm², less than 0.7 nS/μm², less than 1 nS/μm², less than 1.5 nS/μm²,less than 2 nS/μm², less than 5 nS/μm², less than 10 nS/μm², or lessthan 20 nS/μm². The percentage of intact membranes also can bedetermined by inspection using electron microscopy.

For certain uses, one or more nanopores may be created in the membrane.As used herein, a “nanopore” is a pore having a diameter from about 0.3nm to about 999 nm. However, in preferred embodiments, nanopores fromabout 0.3 to about 50 nm are used. The number of nanopores created permembrane may vary depending on the intended application of the membrane.For example, membranes designed for use in determining the sequence ofbases in a polynucleotide may have only a single nanopore per membrane.Alternatively, membranes designed for use in deionization of aqueoussolutions may have a plurality of nanopores per membrane.

EXAMPLES Example 1. Fabrication of Freestanding Ultrathin MoS₂ Membranes

Substrates for nanopore fabrication were 5 mm×5 mm square Si chips witha 100-nm-thick SiN film deposited on a 2.5 μm thick thermal SiO₂ layer.The oxide layer helps to reduce electrical noise. The SiN film wasprotected with a 950 PMMA etch mask, and a small (2 μm×2 μm) region witha pattern of four 600 nm-diameter holes and a central 1.5 μm diameterhole was exposed using Nabity NPGS e-beam writing software on a HitachiS-4800 scanning electron microscope. Exposed PMMA was developed with 3:1isopropyl alcohol and methyl isobutylketone. The SiN film was etched toAFM- and ellipsometry-calibrated thickness in a Technics Micro-RIESeries 800 etcher using sulfur hexafluoride (SF₆) at 300 mTorr and 150W. PMMA was removed using acetone, and chips were cleaned with hotpiranha solution followed by warm water to remove residual PMMA.

MoS₂ membranes were synthesized using an atmospheric-pressure CVDprocess in a split tube furnace with a 35 mm O.D. quartz tube asfollows. The chips were placed in the center of the furnace, suspendedabout 3 mm above MoO₃ powder, and sulfur powder was placed in theupstream region of the furnace chamber.

Ar gas was flowed at 200 sccm through the chamber throughout the growthprocess as well as during the cooling process. First the temperature ofthe furnace was ramped from room temperature up to 300° C. at a rate of30° C./min and held at the target temperature (300° C.) for 15 min toallow for sufficient MoO₃ sublimation. Next, the temperature of thefurnace was raised to 750° C. at a rate of 3° C./min, and sulfurizationwas allowed to proceed for 90 minutes. After that, the furnace wascooled down to room temperature under the continued flow of Ar gas,through the complete opening of the hood of the furnace.

Example 2. Structural Characterization of MoS₂ Membranes

FIG. 2A shows bright-field (BF) TEM images of freestanding MoS₂membranes synthesized, without a substrate, onto micron-scale holesprefabricated in a thin sheet of SiN. Panels (i)-(iv) of FIG. 2A showhigh magnification TEM images of four different MoS₂ membrane devices.Some holes are partially covered with multiple layers of MoS₂, whichpossibly could be due to the insufficient nucleation time during CVD. Itis noteworthy that unintentional wrinkles could be seen in some MoS₂membranes grown across holes, which may be due to stress exerted on themembranes as they freely suspend over the free aperture (see, e.g., FIG.2A(iii)). Different domains of monolayer and multilayer MoS₂ wereobserved in membranes grown across submicron aperture regions.

FIG. 2B shows high resolution TEM (HRTEM) images of the MoS₂ membraneanalyzed in the highlighted region as depicted in FIG. 2A(i) with adashed box. In FIG. 2B it is clear that there were still someincompletely nucleated sites, as highlighted in FIG. 2B(iii) with adashed box. In FIG. 2B(ii), monolayer and bilayer domains of MoS₂ canclearly be seen in the freestanding membrane across an area ofapproximately 6 nm×6 nm. Partially nucleated or incompletely nucleatedsites can also be observed in FIG. 2B(ii). FIG. 2B(iii) shows an HRTEMimage of single layer MoS₂ membrane corresponding to the domainhighlighted in the dashed box in panel (ii). The upper inset shows thecorresponding diffractogram of the image, which further verifies theexistence of monolayer MoS₂ in the region highlighted with the dashedbox in FIG. 2B(ii). The line-profile was manipulated by scanning across10 lattice points (as depicted in FIG. 2B(iii)), which gave a latticeconstant of MoS₂ in the (100) plane of 0.27 nm (bottom inset). FIG.2B(iv) shows an HRTEM image of a bilayer MoS₂ domain corresponding tothe area highlighted in the dashed box in FIG. 2B(ii). The two hexagonallattice structures next to each other corresponding to two layers ofMoS₂ can be seen vividly in FIG. 2B(iv). The inset illustrates thecorresponding diffractogram of bilayer MoS₂ membrane.

FIG. 2C shows BF-TEM images of a device with a five submicron holepattern after MoS₂ growth, where four holes are completely covered withMoS₂ membranes. The inset of FIG. 2C(i) shows the perforated substratewith an e-beam written five-hole pattern before MoS₂ growth. Panels(ii)-(iv) of FIG. 2C show BF-TEM images of one of the membraneshighlighted in FIG. 2C(i) with a dashed box. These CVD-grownfreestanding MoS₂ membranes contain different numbers of layerslocalized on the membrane as seen in FIG. 2C(ii). Unintentionallygenerated wrinkles in the MoS₂ membranes can be seen in FIG. 2C(iii),which is likely due to strain applied to the freestanding MoS₂ membranesacross the free aperture. It is noteworthy that there was a preferenceof growing MoS₂ membranes across cracks that were generated during thee-beam writing process and subsequently developed in CVD temperatureramping (not shown).

FIG. 3A shows an STEM image of the same sample shown in FIG. 2A(i).According to FIG. 3A, MoS₂ membrane was grown 100% of the time in thecrater side of the membrane. FIG. 3B illustrates the same membraneimaged in the backscattering mode (SE mode) from the crater side, whichfurther verifies that MoS₂ membrane was completely been grown on thecrater side, and that the “top” of the sample is the membrane side onwhich there is no MoS₂. This is an interesting observation, because thechip was placed facing membrane side down during CVD operation, wherebythe chip was suspended about 3 mm above the MoO₃ powder. Thereforehaving MoS₂ completely grown on the crater side (and not on the membraneor top side) explains the growth mechanism of MoS₂ across a perforatedsubstrate. One possible explanation is that sublimated MoO₃ leaksthrough the apertures in the SiN membrane and precipitates onto thecrater side of the membrane due to the temperature gradient between topand bottom sides of the chip. Sulfurization takes place with the flow ofsublimated S placed in the upstream portion of the chamber, whichresults in fabricating MoS₂ sheets across the apertures in thesubstrate. This proposed mechanism is further verified from FIG. 2D,panels (i)-(iv), where there is a higher affinity in growing MoS₂ sheetsacross sub micrometer slits in SiN freestanding window. FIG. 3C shows ahigh-resolution STEM image of one of the freestanding MoS₂ membraneshighlighted in FIG. 3A with a dashed box, which clearly demonstratessome Moiré patterns. The FFT collected in the vicinity of the Moirépatterns (inset, FIG. 3C) confirms that it is bilayer MoS₂, where twosheets are slightly rotated on top of each other.

Raman spectroscopy measurements were carried out in the vicinity of themiddle hole in the five-hole pattern (highlighted with dashed box inFIG. 2A) to probe the thickness as well as the crystal quality of theas-grown freestanding MoS₂ membranes (FIG. 4). Raman spectroscopy wascarried out using a Jobin Yvon LabRam HR800 spectrometer attached to anOlympus BH2 microscope. MoS₂ AND MoSe₂ membranes were imaged using aJEOL 2010FEG transmission electron microscope operating in bright-fieldmode at 200 kV, and STEM images were collected using a Hitachi HD 2700at 200 kV, Cs-corrected. Two major Raman features are prominent in theresulting Raman spectrum in FIG. 3A: E2g1 (383 cm⁻¹), which correspondsto an in-plane mode resulting from the opposite vibration of two S atomswith respect to the Mo between them, and A1g (406 cm⁻¹), which isattributed to the out-of-plane vibration of only S atoms in oppositedirections. [55-57] The frequency-shift difference between E2g1 and A1gmodes is correlated to the number of layers in the multilayer MoS₂membranes. [58] According to the frequency-shift difference (about 23cm-1) between the two modes, the center hole (about 2 μm) was mostlycovered with the 2-3 layer thick MoS₂ membranes.

Example 3. Electrical Characterization of MoS₂ Membranes ContainingNanopores

Following optimization of hole-free membrane growth, complete MoS₂membranes were grown on several devices, and a TEM beam was used tofabricate nanopores in these membranes in order to study ion transportthrough the pores. Because of the extremely thin membrane structure,only brief (about 1-2 sec) exposure times using a focused beam weresufficient to produce nanopores; great care was taken to avoid largepore formation, e.g., by reduction of spot size and beam current.

Following the fabrication of several pores of different diameters, thechips were assembled into a custom-made PTFE cell as shown in FIG. 6A.Prior to obtaining measurements, a chip was glued onto the top PTFEportion of the cell using a quick-curing elastomer, and a second layerof glue was applied to the membrane such that only about 1 mm² wasexposed, in order to minimize capacitance-mediated noise. Afterelastomer curing, the cell was assembled, the cis and trans compartmentswere filled with 0.40 M KCl electrolyte buffered to pH 8.0 using 10 mMTris (G_(bulk)=50 mS/cm), and a pair of Ag/AgCl wire electrodes wasimmersed in the chambers. The electrodes were connected to a ChimeraInstruments high-bandwidth amplifier. FIG. 6B shows the current-voltageresponse of the MoS₂ membranes with pores of various diameters. While noappreciable current was measured for the membrane without pores linearcurrent/voltage responses were observed for the three nanopores tested.The responses were characteristic of ion-conducting nanopores. Linearfitting of the slopes of the curves yielded the membrane conductance (G)values which are reported in the legend of FIG. 6B. The inset TEM image(JEOL 2010FEG operating in bright-field mode at 200 kV) shows severalnanopores fabricated adjacent to one another using an electron beam,ranging in diameter from 1 to 5 nm.

To rationalize the observed conductance levels to these pore diameters,the theoretically expected conductance values for circular nanopores ofideal diameter d are plotted in FIG. 6C. The values for MoS₂ membranesof quantized thicknesses in the range of 1-4 layers (where each layer is0.8 nm thick), are also shown in FIG. 6C. To obtain these curves, theaccess resistance in ultrathin membranes was taken into account,yielding the conductivity G for a MoS₂ membrane containing a pore ofdiameter d as described in Equation (1)

G(d)=σ(4nh/πd ²+1/d)⁻¹  (1)

where σ is the bulk electrolyte conductivity, n is the number of MoS₂layers, and h is the thickness of a monolayer (0.8 nm). In FIG. 6C theconductance for three MoS₂ membranes that contained no fabricatednanopores are also plotted, in which the mean conductance was 0.43 nS, afactor of 35 smaller than the conductance of the 2.8 nm pore. Overall,the experimental data indicated pores that of 1-2 layers thickness,apart from a small negative deviation for the larger pore, which mostlikely stems from about 10% error in pore diameter.

Next, the ion-current noise exhibited by nanopores in MoS₂ membranes wasdetermined and compared to that of nanopores in transfer-free graphenemembrane (produced as described in WO 2015/077751, which is incorporatedherein by reference). DC current values were very stable, withpeak-to-peak noise values of about 400 pA at 200 kHz low pass filtersetting. Power spectral density plots are shown in FIG. 7A for differentapplied voltages in range 0-200 mV. The pores exhibited typical 1/fnoise regions that decrease with frequency until overwhelmed bycapacitive noise at f>10⁴ Hz, which is dampened using the 200 kHzdigital low-pass filter (shoulders on right). The 1/f noise in the MoS₂membranes was atypical of 2D pores. In comparison, graphene pores (seeFIG. 7B), due to their more hydrophobic nature and charge fluctuationsin the material, displayed larger 1/f current noise values than MoS₂.

Table 1 displays noise values for pores in membranes made of 2Dmaterials. Heerema and co-workers, as well as Merchant and co-workers,reported for a transferred graphene pore noise density of about 10⁻⁴nA²/Hz at a frequency of 100 Hz, whereas Waduge found for atransfer-free graphene pore a noise value of about 10⁻⁵ nA²/Hz at 200mV. In contrast, for MoS₂ and SiN pores of similar conductance valuesand voltages, the present inventors observed noise densities at 100 Hzbelow 10⁻⁶ and about 10⁻⁷ nA²/Hz, respectively. This value for thepresent MoS₂ membranes is lower than the noise reported by Feng andco-workers for a transferred MoS₂ pore. Recently, 1/f noise in graphenehas been attributed to mechanical fluctuations in the thin material.Since lower noise levels also have been observed in transfer-freegraphene than in transferred graphene, it is apparent that the evenlower noise exhibited by the present polycrystalline MoS₂ membrane growndirectly on apertures is likely a combination of superior mechanicalstability afforded by the direct growth and a material-specific lownoise of MoS₂.

TABLE 1 1/f Ionic Noise Properties For Transferred And Direct-Growth 2DPores Reference 2D Nanopore Noise at 100 Hz, 200 mV Hereema et al. (1)10⁻⁴ nA²/Hz, transferred graphene Merchant et al. (2) 10⁻⁴ nA²/Hz,transferred graphene Waduge et al., 2014 (3) 10⁻⁵ nA²/Hz, transfer-freegraphene Waduge et al., 2015 (4) 10⁻⁶ nA²/Hz, transfer-free MoS₂ Feng etal. (5) 10⁻⁴ nA²/Hz, transferred MoS₂ (1) Heerema, S. J.; Schneider, G.F.; Rozemuller, M.; Vicarelli, L.; Zandbergen, H. W.; Dekker, C. 1/fNoise in Graphene Nanopores. Nanotechnology 2015, 26, 074001. (2)Merchant, C. A., et al. DNA Translocation through Graphene Nanopores.Nano Lett 2010, 10, 2915-21. (3) Waduge, P.; Larkin, J.; Upmanyu, M.;Kar, S.; Wanunu, M. Programmed Synthesis of Freestanding GrapheneNanomembrane Arrays. Small 2014, 11, 597-603. (4) Waduge, P.; Bilgin,I.; Larkin, J.; Henley, R. Y.; Goodfellow, K.; Graham, A. C.; Bell, D.C.; Vamivakas, N.; Kar, S.; Wanunu, M. Direct and Scalable Deposition ofAtomically Thin Low-Noise MoS₂ Membranes on Apertures. ACS Nano 2015, 9,7352-9. (5) Feng, J., et al. Electrochemical Reaction in Single LayerMoS₂: Nanopores Opened Atom by Atom. Nano Lett 2015, 15, 3431-8.

Example 4. Detection of Transport of DNA Molecules Through Nanopores inMoS₂ Membranes

The utility of the present MoS₂ containing nanopores in DNA transportexperiments was tested by studying the transport of single-stranded DNA(ssDNA) through a MoS₂ pore. Rather than using TEM fabrication, for thisstudy the recently described electrochemical reaction (ECR) process wasused. [59] Briefly, a voltage of 1 V was applied for 10-15 s, afterwhich a jump in the membrane conductance was observed, and the voltagewas turned off.

After measuring a pore conductance of about 5 nS, a sample of 153-merssDNA was added to a total concentration of 20 nM, a 200 mV voltage wasapplied, and current traces were recorded. A sample 3-s current trace isshown in FIG. 9A, which displays a stochastic set of downward currentpulses, each indicating the transport of an individual DNA moleculethrough the pore. Below the continuous current trace in FIG. 8A areshown concatenated sets of events that were analyzed using Pythionsoftware. In FIG. 8B is shown a scatter plot of the fractional currentblockade (defined as the ratio of the spike mean amplitude to the openpore current) vs. dwell time for the 744 events in the experiment.Because of the 200 kHz bandwidth, events below 3 μs are significantlydistorted and therefore were discarded from the analysis. Histograms ofboth parameters are also shown above and to the right of the scatterplots, from which mean dwell time was determined as 16 μs and meanfractional current blockade as 26%. On the basis of the values of theopen pore current (1.32 nA at 200 mV) and the mean blockade values, theeffective pore diameter and thickness were estimated as 2.3 nm and twoMoS₂ layers (1.6 nm), respectively. Given the relatively large pore sizeas compared with the nominal diameter of ssDNA (about 1.3 nm), the meantransport velocity of 0.1 μs/bp is reasonable and in accordance with aprior study. [60]

Finally, the data in FIG. 8B shows many events with dwell times (td)below 10 μs, which makes their detection challenging. However, becausethe mean capture rate was 0.95 s⁻¹ nM⁻¹ in the present experiment, and amean capture rate of 0.02 s⁻¹ nM⁻¹ was obtained for a 1.7 nm diameterHfO₂ pore under similar conditions, [61] it is concluded that DNAcapture is efficient in a MoS₂ pore.

Example 5. Detection of Transport of Protein Molecules Through Nanoporesin MoS₂ Membranes

Calmodulin transport was measured through an ultrathin MoS₂ membranecontaining a nanopore. The methodology was similar to that used inExample 4 to observe ssDNA transport, except that a larger pore diameterof 22 nm was used. FIG. 9A shows a continuous 1.5 s long current vs.time trace for the transport of 100 nM calmodulin through the 22nm-diameter MoS₂ nanopore at 100 mV bias voltage applied at the transside. Downward spikes correspond to the translocation or interaction ofcalmodulin with the pore. The inset shows an expanded view ofrepresentative events. FIG. 9B shows a histogram of time intervalsbetween events. The capture rate (R_(c)) of calmodulin translocations isshown in the legend, which is the inverse of the time constant of thetime interval distribution (solid line). FIG. 9C shows a scatter plot ofcurrent blockades vs. dwell times for 165 calmodulin translocationevents (sampling rate=4.2 MHz, low-pass filtered at 50 kHz, T=25° C.,0.4 M KCl, pH 7.8).

Example 6. Fabrication of MoSe₂ Membrane

6 mg of Se powder was added to one of the quartz boats and 2 mg of MoO₂powder to the other boat. The Se boat was placed in the upstream regionof the furnace while the MoO₂ boat was kept in the center of thefurnace. The furnace was purged with 10 sccm H₂ for 30 min and then thetemperature of the furnace was raised to 300° C. at a rate of 15° C./minunder flow of 125 sccm Ar. The furnace was held at 300° C. for 10 minand then raised to 650° C. at a rate of 5° C./min. The furnace was heldat 650° C. for 30 min, and then the hood of the furnace was opened andand the system allowed to cool to room temperature after 30 min underthe flow of 10 sccm H₂ and 125 sccm Ar. FIG. 4B shows Ramancharacterization of the MoSe₂ membrane.

As used herein, “consisting essentially of” does not exclude materialsor steps that do not materially affect the basic and novelcharacteristics of the claim. Any recitation herein of the term“comprising”, particularly in a description of components of acomposition or in a description of elements of a device, can beexchanged with “consisting essentially of” or “consisting of”.

While the present invention has been described in conjunction withcertain preferred embodiments, one of ordinary skill, after reading theforegoing specification, will be able to effect various changes,substitutions of equivalents, and other alterations to the compositionsand methods set forth herein.

This application claims the priority of U.S. Provisional ApplicationNos. 62/118,795 filed 20 Feb. 2015 and entitled “Aperture-LimitedFabrication of Freestanding MoS₂ Membranes” and 62/119,675 filed 23 Feb.2015 and entitled “Aperture-Limited Fabrication of Freestanding MoS₂Membranes”. Both provisional applications are hereby incorporated byreference in their entirety.

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What is claimed is:
 1. A device comprising (i) an ultrathin membranecomprising a two-dimensional transition metal dichalcognide materialcontaining a nanopore, and (ii) a sheet of solid state material havingan aperture, wherein the membrane spans the aperture and is attached toa surface of the sheet in an area surrounding the aperture, and whereineach nanopore has a diameter in the range from about 0.3 nm to about 50nm.
 2. The device of claim 1, wherein the two-dimensional transitionmetal dichalcogenide material is selected from the group consisting ofGaS, GaSe, InS, InSe, HfS₂, HfSe₂, HfTe₂, MoS₂, MoSe₂, MoTe₂, NbS₂,NbSe₂, NbTe₂, NiS₂, NiSe₂, NiTe₂, PdS₂, PdSe₂, PdTe₂, PtS₂, PtSe₂,PtTe₂, ReS₂, ReSe₂, ReTe₂, TaS₂, TaSe₂, TaTe₂, TiS₂, TiSe₂, TiTe₂, WS₂,WSe₂, WTe₂, ZrS₂, ZrSe₂, and ZrTe₂.
 3. The device of claim 1, whereinthe ultrathin membrane consists essentially of from one to severalatomically thin sheets of the two-dimensional material.
 4. The device ofclaim 3, wherein the thickness of the ultrathin membrane is 1-2 atomiclayers.
 5. The device of claim 1, wherein the ultrathin membrane has adensity of holes and atomic vacancies in the range from 0 to about 10per nm².
 6. The device of claim 1, wherein the ultrathin membrane has abackground specific conductance, absent nanopores, of less than about0.2 nS/μm².
 7. The device of claim 1, wherein the ultrathin membranespans a plurality of apertures in the solid state material.
 8. Thedevice of claim 7, wherein the plurality of apertures is arranged in atwo-dimensional array.
 9. The device of claim 7, wherein the ultrathinmembrane comprises one or more nanopores within each aperture, andwherein each of said one or more nanopores has a diameter in the rangefrom about 0.3 nm to about 50 nm.
 10. The device of claim 1, wherein thesolid state material comprises a material selected from the groupconsisting of silicon nitride, silicon dioxide, hafnium oxide, titaniumoxide, and aluminum oxide and has a thickness in the range from about 5nm to about 10 μm.
 11. The device of claim 1, wherein the nanopore hasan ion current noise level of less than 400 pA at 200 kHz bandwidth. 12.A method of detecting a molecule, the method comprising the steps of:(a) providing the device of claim 1 comprising electrolyte solution onboth sides of the ultrathin membrane, an electrode in each electrolytesolution, and a device for measuring ionic currents through thenanopore, wherein the electrolyte solution on one side of the ultrathinmembrane comprises said molecule for detection; (b) measuring a baselineionic current through said nanopore; and (c) observing blockage of thebaseline ionic current by said molecule.
 13. The method of claim 12,wherein the molecule is a nucleic acid or a protein.
 14. The method ofclaim 12, wherein the molecule is detected as it moves through thenanopore of said ultrathin membrane.
 15. The method of claim 12, whereina nucleotide sequence or an amino acid sequence of the molecule isdetermined.
 16. The method of claim 12, wherein a protein is detected,and the protein reduces the ionic current through the nanopore for about2 msec to about 5 msec.
 17. The method of claim 12, wherein theultrathin membrane is functionalized in a region surrounding thenanopore with a functionalization moiety having a binding affinity forsaid molecule.
 18. The method of claim 17, wherein the functionalizationmoiety is an enzyme or an antibody.
 19. The method of claim 12, whereinat least one of said electrolyte solutions comprises an ionic species,the other of said electrolyte solutions comprises a fluorescentindicator that binds said ionic species and changes its fluorescence inresponse thereto, and a current through the nanopore carried by said ionis detected via the fluorescence of the indicator.
 20. The method ofclaim 19, wherein the ion is Ca²⁺.